Question: Simplify the following expression: $ a = \dfrac{t - 10}{t - 6} - \dfrac{-7}{3} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{t - 10}{t - 6} \times \dfrac{3}{3} = \dfrac{3t - 30}{3t - 18} $ Multiply the second expression by $\dfrac{t - 6}{t - 6}$ $ \dfrac{-7}{3} \times \dfrac{t - 6}{t - 6} = \dfrac{-7t + 42}{3t - 18} $ Therefore $ a = \dfrac{3t - 30}{3t - 18} - \dfrac{-7t + 42}{3t - 18} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{3t - 30 - (-7t + 42) }{3t - 18} $ Distribute the negative sign: $a = \dfrac{3t - 30 + 7t - 42}{3t - 18}$ $a = \dfrac{10t - 72}{3t - 18}$